Add maxAwaitTimeMs tests

[noisersup]

Description

Closes #2983.

Readiness checklist

• I added/updated unit tests (and they pass).
• I added/updated integration/compatibility tests (and they pass).
• I added/updated comments and checked rendering.
• I made spot refactorings.
• I updated user documentation.
• I ran task all, and it passed.
• I ensured that PR title is good enough for the changelog.
• (for maintainers only) I set Reviewers (@FerretDB/core), Milestone (Next), Labels, Project and project's Sprint fields.
• I marked all done items in this checklist.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (44500e7) 74.22% compared to head (4eb36a5) 74.39%.
Report is 12 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3968      +/-   ##
==========================================
+ Coverage   74.22%   74.39%   +0.16%     
==========================================
  Files         330      329       -1     
  Lines       25960    25881      -79     
==========================================
- Hits        19269    19253      -16     
+ Misses       5556     5478      -78     
- Partials     1135     1150      +15     

see 24 files with indirect coverage changes

Flag	Coverage Δ
filter-false	?
filter-true	70.90% <ø> (-0.12%)	⬇️
hana-1	?
integration	70.90% <ø> (-0.14%)	⬇️
mongodb-1	5.29% <ø> (+0.12%)	⬆️
mysql-1	?
postgresql-1	50.18% <ø> (-12.97%)	⬇️
postgresql-2	52.11% <ø> (+1.85%)	⬆️
postgresql-3	50.62% <ø> (-1.48%)	⬇️
sqlite-1	49.35% <ø> (-12.82%)	⬇️
sqlite-2	51.20% <ø> (+1.82%)	⬆️
sqlite-3	49.82% <ø> (-1.47%)	⬇️
unit	30.76% <ø> (+0.06%)	⬆️

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[AlekSi]

On hold for now

[AlekSi]

dummy review to remove notification